Make sure the new owner of the App is in the team or add her/him if you need to.
In case if you want to transfer the ownership to an Organization,
you have to be part of the Organization.

Click the Transfer ownership button next to your name

After selecting the new owner from the dropdown, click on the purple button that says
Transfer ownership to <Username>, and you are done!

Good to know: Do you want to remain the connected services user?

If you enable the Do you want to remain the connected services user? option in the Transfer popup,
then during the transfer you'll be explicitly marked as the "connected services" user for the app.

The "connected services" user specifies which Team Member's service connections / accounts
connected to his/her Bitrise user should be used when Bitrise tries to communicate
with another service (GitHub, Bitbucket, ...), for example to send back build status information,
or to register a new SSH key automatically.

Admins of an app can change this any time on the Settings tab of the app.